Question

Show that if $N$ is connected non-compact, orientable n-dimensional manifold, then $H_{n}(N; \mathbb{Z}) = 0.$

score 120 · Answer 1 · 2026-02-23 02:59:21

120

Views

Show that if $N$ is connected non-compact, orientable n-dimensional manifold, then $H_{n}(N; \mathbb{Z}) = 0.$

Published on 23 Feb 2026 - 2:59

score 53 · Answer 2 · 2026-03-25 22:03:06

53

Views

Show that $M$ is R-orientable for any commutative ring $R.$

Published on 25 Mar 2026 - 22:03

score 152 · Answer 3 · 2026-04-05 08:10:52

152

Views

Is $S^n \vee S^n$ a smooth manifold?

Published on 05 Apr 2026 - 8:10

score 844 · Answer 4 · 2026-03-26 14:33:24

844

Views

Stokes Theorem: manifolds vs. chains

Published on 26 Mar 2026 - 14:33

score 420 · Answer 5 · 2026-03-25 14:27:33

420

Views

An orientable surface that cannot be embedded into $\Bbb R^3$?

Published on 25 Mar 2026 - 14:27

score 116 · Answer 6 · 2026-03-31 23:32:26

116

Views

Calculating the integral of a $1$-form

Published on 31 Mar 2026 - 23:32

score 59 · Answer 7 · 2026-03-28 20:08:13

59

Views

Existence of criteria for extension of action of embedded circles in a topological d-manifold.

Published on 28 Mar 2026 - 20:08

score 281 · Answer 8 · 2026-04-05 08:08:56

281

Views

Two Charts Compatible with an Atlas

Published on 05 Apr 2026 - 8:08

score 187 · Answer 9 · 2020-04-19 21:51:24

187

Views

Dimension of a Component of a Topological Space

Published on 19 Apr 2020 - 21:51

score 178 · Answer 10 · 2026-03-25 07:45:49

178

Views

How do you identify the tangent space of the Jacobian variety with differential forms of the first kind?

Published on 25 Mar 2026 - 7:45

score 33 · Answer 11 · 2026-03-27 13:48:30

33

Views

Derivative of the map $\mathbb{R}^9 \rightarrow \mathbb{R}^6$ $f(A)=A A^{T}-I$ Has Linearly Independent Columns When $A$ Orthogonal

Published on 27 Mar 2026 - 13:48

score 71 · Answer 12 · 2026-04-05 08:13:15

71

Views

Questions on the implications of Condition $(2)$ on $\{U_i,\alpha_i\}$ being an atlas for $X$ (image of $\alpha_i$ contained in Banach space)

Published on 05 Apr 2026 - 8:13

score 58 · Answer 13 · 2020-04-21 14:22:18

58

Views

What is the precise definition of a 'landscape' in the context of differential geometry on manifolds

Published on 21 Apr 2020 - 14:22

score 489 · Answer 14 · 2020-04-21 16:56:05

489

Views

Is every manifold homeomorphic to a subset of some Euclidean space?

Published on 21 Apr 2020 - 16:56

score 109 · Answer 15 · 2026-03-26 09:42:21

109

Views

Visualization of the proof in Lee's Smooth Manifolds book that every open cover has a regular refinement

Published on 26 Mar 2026 - 9:42

List Question

Show that if $N$ is connected non-compact, orientable n-dimensional manifold, then $H_{n}(N; \mathbb{Z}) = 0.$

Show that $M$ is R-orientable for any commutative ring $R.$

Is $S^n \vee S^n$ a smooth manifold?

Stokes Theorem: manifolds vs. chains

An orientable surface that cannot be embedded into $\Bbb R^3$?

Calculating the integral of a $1$-form

Existence of criteria for extension of action of embedded circles in a topological d-manifold.

Two Charts Compatible with an Atlas

Dimension of a Component of a Topological Space

How do you identify the tangent space of the Jacobian variety with differential forms of the first kind?

Derivative of the map $\mathbb{R}^9 \rightarrow \mathbb{R}^6$ $f(A)=A A^{T}-I$ Has Linearly Independent Columns When $A$ Orthogonal

Questions on the implications of Condition $(2)$ on $\{U_i,\alpha_i\}$ being an atlas for $X$ (image of $\alpha_i$ contained in Banach space)

What is the precise definition of a 'landscape' in the context of differential geometry on manifolds

Is every manifold homeomorphic to a subset of some Euclidean space?

Visualization of the proof in Lee's Smooth Manifolds book that every open cover has a regular refinement

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